$SO(n,1)$面群上基本群表象的形变与地震
Deformations of fundamental group representations and earthquakes on $SO(n,1)$ surface groups
摘要：
本文构造了表示$π_1(M)\rightarrow G$的一类变形，其中$G$是任意李群，$M$是包含CAT（0）流形的一大类流形.变形是基于余维1超曲面在一定条件下的定义，也是基于这种超曲面的不交并，即多超曲面。我们证明了沿不相交超曲面变形的交换性。作为应用，我们认为Anosov表面组在$SO(n,1)$，并表明，该结构可以不断扩展到测量层合板，从而获得这些表面组的地震变形。
英文摘要：
In this article we construct a type of deformations of representations $π_1(M)\rightarrow G$ where $G$ is an arbitrary lie group and $M$ is a large class of manifolds including CAT(0) manifolds. The deformations are defined based on codimension 1 hypersurfaces with certain conditions, and also on disjoint union of such hypersurfaces, i.e. multi-hypersurfaces. We show commutativity of deforming along disjoint hypersurfaces. As application, we consider Anosov surface groups in $SO(n,1)$ and show that the construction can be extended continuously to measured laminations, thus obtaining earthquake deformations on these surface groups.
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